Question
50 students are randomly selected and 4 own cats. If there are 800 students, use a proportion to estimate how many of them own cats.
Answers
GPT-4o mini
To estimate the number of students who own cats based on the sample, we can set up a proportion. From the sample of 50 students, 4 own cats. We want to find the expected number of students who own cats in a total student population of 800.
First, we set up the proportion based on the sample:
\[
\frac{\text{Number of students with cats in sample}}{\text{Total students in sample}} = \frac{\text{Estimated number of students with cats in population}}{\text{Total students in population}}
\]
Substituting the numbers we have:
\[
\frac{4}{50} = \frac{x}{800}
\]
where \( x \) is the number of students who own cats in the entire population of 800 students.
Now we can cross-multiply to solve for \( x \):
\[
4 \times 800 = 50 \times x
\]
\[
3200 = 50x
\]
Next, we divide both sides by 50 to isolate \( x \):
\[
x = \frac{3200}{50} = 64
\]
Therefore, we estimate that approximately **64 students** out of 800 own cats.
First, we set up the proportion based on the sample:
\[
\frac{\text{Number of students with cats in sample}}{\text{Total students in sample}} = \frac{\text{Estimated number of students with cats in population}}{\text{Total students in population}}
\]
Substituting the numbers we have:
\[
\frac{4}{50} = \frac{x}{800}
\]
where \( x \) is the number of students who own cats in the entire population of 800 students.
Now we can cross-multiply to solve for \( x \):
\[
4 \times 800 = 50 \times x
\]
\[
3200 = 50x
\]
Next, we divide both sides by 50 to isolate \( x \):
\[
x = \frac{3200}{50} = 64
\]
Therefore, we estimate that approximately **64 students** out of 800 own cats.